Amazon.com Inc. Chief Executive Jeff Bezos is buying the Washington Post for $250 million in an out-of-the-blue deal that captures the newspaper industry's economic decline and the shift of power from old media to Silicon Valley.

The sale puts one of the most famous newspapers in the U.S.—the publication credited with breaking the Watergate scandal that led to President Nixon's resignation almost 40 years ago—in the hands of a Web...